Hexagonal tetraswirlprism

Hexagonal tetraswirlprism
(OFF file)
Rank	4
Type	Isogonal
Elements
Cells	288 phyllic disphenoids, 144 rhombic disphenoids, 48 hexagonal gyroprisms
Faces	576+576 scalene triangles, 48 hexagons
Edges	144+144+288+288
Vertices	144
Vertex figure	12-vertex polyhedron with 4 tetragons and 12 triangles
Measures (based on hexagonal duoprisms of edge length 1)
Edge lengths	Short side edges (144): ${\sqrt {4-{\sqrt {6}}-{\sqrt {2}}}}\approx 0.36819$
	Medium side edges (144): ${\sqrt {3}}-1\approx 0.72305$
	Long side edges (288): ${\sqrt {\frac {8-3{\sqrt {2}}-{\sqrt {6}}}{2}}}\approx 0.80866$
	Edges of hexagons (288): 1
Circumradius	${\sqrt {2}}\approx 1.41421$
Central density	1
Related polytopes
Dual	Hexagonal tetraswirltegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(I2(24)≀S2)+/4, order 576
Convex	Yes
Nature	Tame

The hexagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 48 hexagonal gyroprisms, 144 rhombic disphenoids, and 288 phyllic disphenoids. 4 hexagonal gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the icositetragonal duoprism. It is the fourth in an infinite family of isogonal hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {1}{\sqrt {4-{\sqrt {6}}-{\sqrt {2}}}}}$ ≈ 1:2.70868.